Michael V. Nathal and David L. Krause

Glenn Research Center, Cleveland, Ohio

Nathan G. Wilmoth

Vantage Partners, LLC, Brook Park, Ohio

Brett A. Bednarcyk

Glenn Research Center, Cleveland, Ohio

Eric H. Baker

Connecticut Reserve Technologies, Inc., Cleveland, Ohio

Three-Dimensional Cellular Structures Enhanced

by Shape Memory Alloys

NASA/TM—2014-218324

June 2014
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Michael V. Nathal and David L. Krause

Glenn Research Center, Cleveland, Ohio

Nathan G. Wilmoth

Vantage Partners, LLC, Brook Park, Ohio

Brett A. Bednarcyk

Glenn Research Center, Cleveland, Ohio

Eric H. Baker

Connecticut Reserve Technologies, Inc., Cleveland, Ohio

Three-Dimensional Cellular Structures Enhanced

by Shape Memory Alloys

NASA/TM—2014-218324

June 2014

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
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Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2014-218324 1 

Three-Dimensional Cellular Structures Enhanced by 

Shape Memory Alloys 

Michael V. Nathal and David L. Krause 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Nathan G. Wilmoth 

Vantage Partners, LLC 

Brook Park, Ohio 44142 

Brett A. Bednarcyk 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Eric H. Baker 

Connecticut Reserve Technologies, Inc. 

Cleveland, Ohio 44040 

Abstract 

This research effort explored lightweight structural concepts married with advanced “smart” materials 

to achieve a wide variety of benefits in airframe and engine components. Lattice block structures were 

cast from an aerospace structural titanium alloy Ti-6Al-4V and a NiTi shape memory alloy (SMA), and 

preliminary properties have been measured. A finite element-based modeling approach that can rapidly 

and accurately capture the deformation response of lattice architectures was developed. The Ti-6-4 and 

SMA material behavior was calibrated via experimental tests of ligaments machined from the lattice. 

Benchmark testing of complete lattice structures verified the main aspects of the model as well as 

demonstrated the advantages of the lattice structure. Shape memory behavior of a sample machined from 

a lattice block was also demonstrated. 

1.0 Introduction 

The technical literature abounds with lightweight structural concepts using periodic cellular structures 

such as honeycombs and lattice block materials. Honeycombs have been primarily used in lightweight 

sandwich structures and are some of the most efficient (high strength/density) structures in many important 

loading situations such as bending (Ref. 1). Lattice block, consisting of truss architectures (Fig. 1) at a 

micro- or meso-scale, are preferred over honeycombs (Fig. 2) when the loading situations are more threedimensional, or when honeycomb fabrication is not compatible with the desired material selection (Ref. 2). 

Lattice block structures are also damage and defect tolerant (Ref. 3) and can be efficient in heat transfer; for 

example, cooling fluid can be passed though the lattice. In the past five years, an exciting outgrowth of these 

concepts is the development of “auxetic” structures (Fig. 2(b)), which are characterized by negative 

structural Poisson’s ratios (indicating that a structure gets thicker when it is stretched, the opposite of normal 

behavior). Scarpa and co-workers (Refs. 4 to 6) applied an auxetic structure to airfoil shapes (Fig. 3) and 

showed that a wing box with an auxetic core offers high deformability while maintaining structural 

integrity, which is particularly attractive for morphing behavior. High amounts of camber change were both 

predicted and measured. Ju and Summers (Refs. 7 to 10) also showed that auxetic structures have unusually 

high combinations of strength and complianceAuxetics are also projected to have improved impact 

resistance and therefore have relevance to fan containment systems. 
NASA/TM—2014-218324 2 

Figure 1.—Example lattice block unit cell. 

(a) (b)

Figure 2.—Example honeycomb structure configurations: (a) conventional, and (b) auxetic. 

Figure 3.—Auxetic morphing airfoil from Spadoni and Ruzzene (Ref. 5). 

Constructing the cellular structures from shape memory alloys (SMAs) provides even greater 

potential. SMAs can be used in two ways, depending on alloy selection and temperature (Ref. 11). First, 

SMAs can be designed to take advantage of the shape memory effect. Here, the structure can change 

shape as a response to heating and cooling cycles to achieve morphing behavior, or alternately a selfhealing concept where damage from an impact event can be recovered via a thermal treatment. Secondly, 

SMAs can be designed to be superelastic. Extremely high deformations and loads can be achieved while 

still behaving in a reversible manner similar to an elastic response (and thereby allowing long lives and 

durability in fatigue, gust and impact loading situations). 

Prior work on lattice block materials has included work on investment castings to produce net shape 

lattice castings. This allows for parts with complex curvatures to be easily fabricated. Aluminum alloys 

(Ref. 12), nickel-based superalloys (Ref. 3), and titanium alloys (Ref. 13) have been examined. In general, 

the ability of the casting process to produce quality castings was demonstrated, although the tendency for 

porosity resulting from solidification shrinkage was difficult to eliminate. Despite significant casting 

defects, good strength and damage tolerance of the lattice structures have been measured. 
NASA/TM—2014-218324 3 

The purpose of the present work was to explore the structural performance of lattice structures 

fabricated by investment casting. Evaluation of both conventional and auxetic lattices, using both an SMA 

and an aerospace structural Ti alloy (Ti-6wt% Al-4%V) was planned. The castings were produced by 

Transition45 Technologies Inc., Orange, California, which developed the casting process under a Small 

Business Innovative Research contract with NASA (Ref. 14). The details of their casting development are 

considered proprietary and are restricted to the contract reports. This report will cover the mechanical 

property evaluation of the castings produced by T45. Note that auxetic lattice structures were not 

produced in time for inclusion in this report, and therefore no further discussion is provided. 

2.0 Material Processing 

The SMA castings received to date had a higher population of casting defects than T45 would 

normally deliver, but NASA elected to receive these in order to get at least a preliminary indication of 

SMA lattice behavior. Cracks were the most significant defect, and occurred particularly at lattice nodes. 

The particular composition for this work, Ni-50at% Ti, was chosen because of its very high shape 

memory actuation capacity. However, this alloy is not optimally processed by casting, and substantial 

amounts of the deleterious Ti2Ni phase were found during microscopic characterization of the castings. 

Attempts to minimize this embrittling phase by modifying the casting parameters are in progress. If these 

trials are unsuccessful, a new Ni-rich alloy (Ni-49.8at % Ti) may be the best choice for future castings. 

Defects were present in the Ti-6-4 castings also, but at a much lower occurrence than in the SMA 

castings. In general, our experience with the lattice structure test articles revealed that the large surface 

area and configuration of the cellular casting make non-destructive inspection for determining the 

presence of all cracks and defects rather difficult. 

3.0 Ligament Testing 

Both 90and 45ligaments were machined from the Ti-6-4 and SMA lattice blocks in preparation for 

testing, as shown in Figure 4. Note that these test samples included lattice nodes (see circled regions, 

Fig. 4(b)), which are a common site for casting defects. These unconventional geometries required a new 

clamping grip system to be designed to match the ligament shapes in order to test in tension. Duplicate 

tension and compression tests of Ti-6-4 ligaments at 23, 165, and 200 °C were completed. Representative 

stress-strain curves are shown in Figures 5 and 6, respectively. The stress and strain scales are fixed for all 

tests to highlight the change in properties with an increase in test temperature. 

(a) (b)

Figure 4.—(a) Lattice block bulk casting, and (b) machined ligament specimens for tensile testing. 
NASA/TM—2014-218324 4 

(a) 

(b) 

(c) 

Figure 5.—Ti-6-4 tension testing stress-strain curves at (a) 23 C, (b) 165 C, and (c) 200 C. 

 
NASA/TM—2014-218324 5 

(a) 

(b) 

(c) 

Figure 6.—Ti-6-4 compression stress-strain curves at (a) 23 C, (b) 165 C, and (c) 200 C. 

 
NASA/TM—2014-218324 6 

TABLE 1.—SUMMARY OF LIGAMENT TENSILE AND COMPRESSION DATA 

Test 

temp. 

(°C) 

Material Test type Elastic 

modulus 

(GPa)a

Yield stress 

(MPa)b

Ultimate 

strength 

(MPa) 

Poisson’s 

ratio 

Literature source 

or experimental 

data 

23 Ti-6-4 tension 114 897 1000 0.26 to 0.36 Refs. 15 & 16 

165 Ti-6-4 tension 107 700 828 0.26 to 0.36 Refs. 15 & 16 

200 Ti-6-4 tension 105 679 786 0.26 to 0.36 Refs. 15 & 16 

23 Ti-6-4 tension 117 830 929 0.3 as measured 

165 Ti-6-4 tension 105 612 743 0.31 as measured 

200 Ti-6-4 tension 101 562 695 0.31 as measured 

23 Ti-6-4 compression 113 870 x 0.33 as measured 

165 Ti-6-4 compression 109 673 x 0.34 as measured 

200 Ti-6-4 compression 87 642 x 0.34 as measured 

23 Ni-50%Ti compression 36.1 –240 –425 Ref. 17 

23 Ni-50%Ti compression 28 –249 –475 as measured 

165 Ni-50%Ti compression 51 –474 as measured 

200 Ni-50%Ti compression 49 –564 as measured 

a

For compression tests of the Ni-50%Ti material, this is the stress at initial apparent yielding 

b

For compression tests of the Ni-50%Ti material, this is the stress at the finish of reorientation 

A summary of the material properties for Ti-6-4 tests obtained from literature and the averages of this 

testing effort are shown in Table 1. In general, the measured strengths were found to differ only slightly 

from published data (Refs. 15 and 16) for conventionally processed materials. This indicates that the 

casting process produced acceptable microstructures. Some tensile ligaments exhibited early failure, 

which was most likely due to casting defects. Note that the elastic moduli of the 200 °C compression tests 

were lower than expected, because a large percentage of those specimens exhibited buckling failures. 

Duplicate tension and compression testing at 23, 165, and 200 °C were also envisioned for ligaments 

extracted from SMA lattice block panels. Because of the casting problems mentioned previously, only 

compression samples could be extracted from the SMA panels. The representative stress-strain curves for 

these tests are shown in Figure 7. There is scatter in the data. The expected curve shapes are observed, 

however. At room temperature, the stress strain curves exhibit an initial yielding which is considered the 

onset of martensite reorientation and detwinning (Refs. 17 and 18). Martensite reorientation continues at a 

slight hardening rate for approximately 0.5 percent strain, followed by a region with steeply increased 

hardening, which is associated with plastic deformation of the martensite (Refs. 17 and 18). At the higher 

test temperatures, the alloy is austenitic and the yielding behavior corresponds to stress-induced 

martensite and concurrent operation of slip and deformation twinning (Ref. 19). 

For the NiTi base SMAs, a large amount of tensile data is available in the literature but very little data 

is available for compression testing. Room temperature compression testing completed by other NASA 

groups on extruded NiTi (Ref. 17) was located and used for comparison to current as-cast test results in 

Table 1. The moduli from the as-cast specimens from this test effort are lower compared to the extruded 

material by 22.3 percent. Note that the initial yielding and reorientation finish stresses are slightly higher 

than as reported for the extruded material. 

Ligament testing results were used as calibration data for the finite element modeling, as described in 

Figure 8. In addition, the SMA specimen compressed at room temperature was subsequently heated to 

evaluate shape memory behavior. Approximately 3 percent strain was recovered upon heating, which is 

consistent with the expected behavior of the alloy. 
NASA/TM—2014-218324 7 

(a) 

(b) 

(c) 

Figure 7.—NiTi compression stress-strain curves at (a) 23 C, (b) 165 C, and (c) 200 C. 
NASA/TM—2014-218324 8 

(a) 

(b) 

Figure 8.—Ligament test results with material calibration curve fits to existing 

Abaqus constitutive models: (a) Ti-6-4 in tension and compression, and 

(b) SMA in compression. 
NASA/TM—2014-218324 9 

4.0 Model Development 

The purpose of the modeling effort was to ensure that a proper understanding of the physics of lattice 

deformation had been achieved. This then would allow for high confidence in future extrapolations to 

new structures as well as in optimization of the lattice structure geometry for particular applications. Low 

cost evaluation of multiple structural concepts before investing in experimental demonstration efforts 

would be a key benefit. 

A Python script was written to automatically generate Abaqus (Dassault Systèmes) finite element 

models of arbitrary lattice geometries. The script was parametric, so it was quick and efficient to generate 

models for different configurations, run finite element models, and post-process results. The ligaments 

were treated as beams with arbitrary nonlinear material behavior that can also experience nonlinear 

geometric effects. Example lattice geometries generated using the Python script are shown in Figure 9. 

The script was then specialized to generate models of the 4-point bend and flat-wise compression 

tests that were conducted. The acreage ligament cross-section was treated as circular, while the edge 

ligament cross-section was treated as rectangular to match the as-fabricated conditions. Pre-test 

predictions, along with parametric sensitivity studies, were conducted for the 4-point bend configuration 

of the Ti-6-4 lattice. The 4-point bend test article and model geometry are shown in Figure 10. 

After performing a mesh senstivity study to arrive at a globally converged mesh, a parametric 

sensitivity study was performed by varying the material representation, the height of the panel, and the 

ligament diameter. At the time of the pre-test predictions, only tensile ligament test results were available, 

showing some variability. The nonlinear material response was modeled using von Mises plasticity. To 

capture the variability in the tensile test results, two sets of material data were used in the sensitivity 

studies, as shown in Figure 11. 

Variation of the panel height was intended to examine the effect of non-centered ligament nodes in 

the as-built lattice panels. This is shown in Figure 12. To assess the impact of this offset, panel heights 

(distances between face ligament centroids) of 18.0 and 21.5 mm were examined. 

Figure 9.—Actual lattice casting and three sample geometries generated with the Python Script. 

(a) (b)

Figure 10.—(a) 4-point bend test article, and (b) finite element model. 
NASA/TM—2014-218324 10 

Figure 11.—Abaqus plasticity model fit to room-temperature Ti-6-4 

ligament test data that was used to capture the variability of the 

material response.

Figure 12.—Offset between face ligament 

centroids and actual node location.

Figure 13.—Pre-test prediction of Ti-6-4 lattice block 4-point bend response. 

Finally, ligament diameters of 3.25, 3.50, and 3.75 mm were examined to assess the impact of crosssectional area variability, which has been observed in the lattice ligaments. The predicted applied load 

versus bottom center point deflection is plotted in Figure 13, along with deformation contours at various 

points. These two curves represent what was then believed to be the best pre-test predictions while still 

factoring in the variable Ti-6-4 material response shown in Figure 11. The predicted response involved a 

peak, followed by softening as significant buckling of the top face struts was predicted. The model was 

loaded in diplacement control of top face points (Fig. 10) to a maximum of 4 mm, then unloaded. A 

significant amount of permanent set, due to plasticity, was predicted. 

0

100

200

300

400

500

600

700

800

900

1,000

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07

Stress(MPa)

Strain(in/in)

Test:TL_RT_3T

Test:TL_RT_4B

Test:TL_RT_15B

AbaqusPlasticityModel High

AbaqusPlasticityModel Low
NASA/TM—2014-218324 11 

Figure 14.—Full set of parametric simulations on the 4-point bend response of the Ti-6-4 Lattice. 

The full set of results from the parametric study, where panel height, Ti-6-4 material representation, and 

ligament diameter were varied, is shown in Figure 14. These results indicated that panel height and strut 

diameter had a significant effect on the lattice 4-point bend response (changes on the order of 35 percent), 

while the Ti-6-4 material variation examined was minor (changes on the order of 5 percent). This is not 

surprising, as deflection and load carrying capacity in this test configuration are structural in nature—that is, 

governed by rigidity (elastic modulus E times bending moment of inertia I) rather than material stiffness 

(proportional to E) alone and the cross sectional area of each strut. Note that I is highly nonlinear with 

height h: for example, I = bh3

/12 for a plate or laminate, where b is the representative width. 

5.0 Structural Benchmark Testing 

The structural benchmark testing effort included mechanical tests of complete lattice structure test 

articles. By evaluating the mechanical response to prototypical structural loadings, this work provided 

physical evidence of advantages in the lattice cellular structure configuration. Some of these advantages 

were light weight, high efficiency, and inherent structural redundancy. In addition, the testing demonstrated shape memory response in a complex lattice structure, which augmented understanding the effect 

observed in the tests from the simpler geometry of solid uniaxial test coupons. As described in the next 

section, the tests also provided data for verification of the soundness of the model development effort. 

 
NASA/TM—2014-218324 12 

Testing was based on availability of lattice castings. Lattice structures cast in Ti-6-4 were received in 

two configurations: 100 by 100 by 25 mm panels, and a 50 by 200 by 25 mm panel. The former were 

retained for future flat-wise compression testing, while the latter was cut into three long-beam bending 

test articles. Lattice structures cast in the SMA NiTi were also received, in the 100 by 100 by 25 mm 

panel configuration. These were suitable for flat-wise compression tests. All test series were conducted 

isothermally at room temperature (23 °C). 

The first test series was performed on Ti-6-4 Test Article S/N 22C. This test article had overall 

dimensions of 200 by 50 by 25 mm and was 12 by 3 unit cells, composing three longitudinal “trusses.” 

The average strut diameter was 3.505 mm. The long-beam bend test configuration (Fig. 15) on the 50 kN 

MTS (MTS Systems Corporation) load frame was symmetrical. The lower reaction supports were placed 

at two-node locations spaced 180 mm apart, and the upper load rollers were placed at two-node locations 

spaced 72 mm apart. Four-point loading positioned the entire middle span between load rollers under the 

same nominal maximum moment value. In bending, the test article’s structural limits were explored 

through a series of increasing load ramp cycles in displacement control (Fig. 16). Elastic loadings to 

2.224, 4.448, and 13.34 kN total load were completed with almost no measurable nonlinearity or 

hysteresis upon return to zero load. The elastic series was followed by loading to the first observed strut 

failure occurring at 20.01 kN (Fig. 17). 

Figure 15.—Long-beam bend test set-up: lattice 

structure test article is shown mounted in hinged 

four-point load fixtures. 

Figure 16.—Bend test load ramps: a series of bend test 

load ramps were applied to the lattice structure beam. 

Figure 17.—Failure and residual strength tests: after first 

failure, most lattice structure strength remained. 
NASA/TM—2014-218324 13 

With the displacement load ramp continuing to run for a short period, the specimen resisted 

approximately 17.5 kN. Upon unloading, specimen inspection using optical microscopy could not locate a 

suspected fracture. Additional residual strength testing was continued under test machine displacement 

control, until 18.49 kN strength was measured at the second strut failure. With the displacement loading 

continuing to run, residual strength of 12 kN was observed until the machine stroke limit of 5.5 mm 

specimen deflection was reached. Close post-test visual inspection revealed two fractures, one at a node 

and one through a strut. 

The second test series was performed on SMA NiTi Test Article Heat 1131 S/N 2-1. This test panel 

had overall dimensions of 98 by 99 by 26 mm and was five unit cells square. The average strut diameter 

was 3.858 mm. The flat-wise compression strength test was performed first on a 50 kN MTS load frame 

and included a spherical joint fixture with rigid platens to assure uniform loading of all 18 upper and 

18 lower “face sheet” nodes (Fig. 18(a)). Figure 18(b) provides a schematic showing the construction 

features of a spherical joint platen, which allows relative rotation between the upper and lower load 

surfaces. 

In compression, the test frame’s load limit was approached prior to significant deformation or failure 

of the test article. A peak loading of 41.9 kN was recorded at 0.41 mm panel deflection. To further 

explore the load-carrying ability of the SMA test article, a 450 kN-capacity Instron load frame was 

reconfigured with the spherical joint platen fixtures. Upon loading, first failure was identified at 155 kN 

total panel load. An in situ inspection revealed a crack in the specimen’s integrally cast lower perimeter 

tension frame, likely at a pre-existing flaw. Continued higher loading under stroke control demonstrated 

load redistribution capability within the lattice structure, providing additional strength to achieve the peak 

load of 170 kN at 1.6 mm deflection. This deflection correlates to approximately 6 percent structural 

through-thickness deformation (Fig. 19). Note that the use of one linear variable differential transformer 

(LVDT) as positioned to measure displacement between the upper and lower platens may cause error in 

reported deflection if rotation of the spherical joint platen occurs due to unsymmetrical specimen 

stiffness. This may have contributed to the apparent increasing stiffness observed during Test1 Load as 

well as the apparent high stiffness observed upon the initial loading of Test2 Load seen in Figure 19. The 

potential discrepancy may be avoided by use of three LVDT’s to measure planar position changes, or by 

the use of one central LVDT to obtain the average deflection values. Post-test visual inspection revealed 

(a) (b) 

Figure 18.—Flat-wise compression test: (a) lattice test article is mounted between platens, 

with spherical joint fixture beneath specimen, and (b) schematic of spherical joint platens 

construction. 
NASA/TM—2014-218324 14 

Figure 19.—Compression strength test of NiTi lattice: strength and 

deformation were available after the initial break at 155 kN. 

Figure 20.—Compression yield test: the second SMA 

lattice structure test article was loaded in compression to 

produce approximately 2 percent residual deformation. 

Figure 21.—Recovery of strain via the shape memory 

effect: thermal treatment restored 60 percent of the 

initial inelastic strain resulting from compression of 

the test article. 

additional cracks in the upper and lower perimeter tension frames. This altered the structure’s stress 

distribution, placing struts in bending and progressively failing most nodes and cracking many struts at 

mid-length locations. Because of the extensive non-reversible damage, post-test thermal treatment for 

strain recovery (self-healing) was not warranted for this test article. 

The third test series was performed on SMA NiTi Test Article Heat 1131 S/N 6-2. This test panel was 

cast to very similar overall dimensions and geometry as Test Article S/N 2-1. It had overall dimensions of 

98 by 99 by 26 mm and was five unit cells square. The average strut diameter was 3.858 mm. The flatwise compression yield test with strain recovery was performed on the 450 kN-capacity Instron load 

frame configured with the spherical joint and platen fixtures (similar to Fig. 18). In compression at a rate 

of 0.305 mm per minute, a peak load of 101 kN was attained at a deflection of 0.65 mm. This deflection 

corresponds to a 3.1 percent compressive structural strain (Fig. 20). 

No evidence of cracking or failure of the structure was observed. Following release of the load, the 

residual compressive through-thickness strain was 1.95 percent. This value relaxed to 1.58 percent after a 

period of 15 min at room temperature. Post-test heat treatment at 95 °C resulted in strain recovery to 

1.33 percent, while an additional heat treatment at 200 °C for 120 min produced strain recovery to 

0.79 percent. This value of recovery is the equivalent of 60 percent of the initial inelastic deformation 

after release of the load (Fig. 21). This confirms shape memory behavior in the structural lattice.
NASA/TM—2014-218324 15 

6.0 Analytical Verification 

The agreement between the most representative pre-test prediction (for average strut diameter of 

3.5 mm) and the bend test performed on the Ti-6-4 lattice is shown in Figure 22. As shown, the model 

predicted the inital slope and onset of nonlinearity well, but the softening associated with top ligament 

buckling was absent in the test data. In the test, failure occurred in one of the two ligaments in the bottom 

face as shown. Note that no attempt to model this type of ligament fracture had yet been made. The lack 

of softening in the test results indicated that buckling of the top face struts was limited in the test and 

overpredicted in the model. 

In an attempt to explain the discrepancy, compressive ligament test data, which became available 

after the 4-point bend test, was modeled using an existing material model in the Abaqus library (“cast iron 

plasticity model”). This model allows for distinct tensile and compressive material plastic behavior. The 

fit of the model to experimental room-temperature Ti-6-4 ligament data is shown in Figure 8, where now 

the compressive response hardened significantly more than the tensile response (Fig. 8(a)). Switching to 

this material model decreased but did not eliminate the amount of softening in the model (Fig. 23). To 

further suppress the buckling in the top face ligaments, a non-circular ligament cross-section was 

considered in the top face of the lattice only. This simulated the tear-drop shaped cross-section of the 

casting (Fig. 23) and enabled the ligaments to have greater resistance to out-of-plane bending and thus 

greater buckling resistance. For simplicity, a rectangular cross-section was considered as shown in 

Figure 23. 

Figure 22.—Correlation between pre-test prediction and Ti-6-4 lattice block 4-point bend test data. 
NASA/TM—2014-218324 16 

Figure 23 compares the altered model with the experimental data. While the rectangular shape of the 

top face ligaments was not completely representative, this simulation showed that by suppressing 

buckling of the top face ligaments, the test data could be captured. An additional feature that would also 

suppress top face ligament buckling was the thicker ligament sections near the nodes, which was not 

included in the model geometry. This would reduce the free span of the ligaments, which would reduce 

their tendency to buckle. This effect will be examined in the future. 

Finally, a pre-test prediction was made for the flat-wise compression behavior of the SMA lattice. 

The actual casting and the Abaqus model are shown in Figure 24. To simulate the flat-wise compression 

test, the bottom nodes in the model were fixed and the top nodes were displaced downward at a constant 

rate. As a first step, the SMA material was modeled using the Abaqus von Mises plasticity constitutive 

model. The fit of this model to SMA ligament tensile test data is shown in Figure 8. The agreement 

between the pre-test flat-wise compression prediction and experiment is shown in Figure 25. The model 

matched the experiment well for the initial slope and onset of nonlinearity. The model was then slightly 

more compliant than the test data. The model response began to stiffen in association with the SMA 

material stiffening response shown in Figure 8. The model was then not able to converge due to the 

extensive buckling of the lattice internal ligaments. Although this cannot necessarily be considered a 

predicted failure, it did occur at an applied displacement of 1.18 mm, which corresponds closely to the 

applied displacement at first failure in the test (1.16 mm). 

Figure 23.—Correlation of model, altered to suppress top face ligament buckling, with experiment 

for the Ti-6-4 lattice 4-point bend test. 

(a) (b)

Figure 24.—(a) SMA lattice casting, and (b) Abaqus finite element model. 
NASA/TM—2014-218324 17 

Figure 25.—Model prediction and experimental results for SMA lattice in compression. 

7.0 Summary and Conclusions 

This paper explores the performance of lattice block structures and their suitability for aerospace 

applications. Lattice blocks were cast from aerospace structural titanium alloy Ti-6Al-4V and NiTi shape 

memory alloy. Preliminary properties have been measured as a part of this test effort. A finite elementbased modeling approach that can rapidly and accurately capture the deformation response of lattice 

architectures was developed. The Ti-6-4 and SMA material behavior was calibrated via experimental tests 

of ligaments machined from the lattice. Benchmark testing of complete lattice structures verified the main 

aspects of the model as well as demonstrated the advantages of the lattice structure. Shape memory 

behavior of a sample machined from a lattice block was also demonstrated. 

The long-beam bend testing of a Ti-6-4 lattice structure exhibited almost no inelastic behavior for 

loadings to 13.34 kN. This indicates that micro-yielding at local stress risers, if it existed, did not affect 

the overall structural response. After the first and second tensile failures of a strut (or node), much 

strength and deformation capability existed. The strength retention demonstrates the advantages of the 

highly redundant lattice structure the availability of alternative load paths afetr a failure. In bending, the 

top compression struts plastically deformed and buckled before the first bottom strut tensile rupture was 

discovered. For aerospace service this is a valuable benefit, because it provides an observable sign of 

distress before structural failure. Necking deformation at strut tensile breaks indicated fully developed 

plasticity above the Ti-6-4 material’s yield point. As a testing consideration, the observed large specimen 

deformations required careful selection of the appropriate load and support fixtures to permit free 

rotations and lateral movements. 

Flat-wise compression testing of SMA NiTi lattice structures indicated insensitivity to defects for this 

load case. The test articles had several known casting defects present but until failure of the integral 

tensile frame in one case, the defects did not affect test results to a measurable degree. In the first 

compression test article, 0.2 mm of deformation were unrecovered upon unloading from 41.9 kN during 

the first load cycle. Local yielding resulting from non-planar outer contact surfaces of the panel are the 
NASA/TM—2014-218324 18 

most likely cause for the unrecovered deformations. Similarly, this may be responsible for the condition 

of initial increasing stiffness with load during the compression tests. For the first compression test article, 

the compliance curve of the second load cycle to 41.9 kN was greatly different than for the first cycle. 

This is a unique behavior characteristic of the SMA material. For the second compression test article, the 

recovery of 60 percent of the initial inelastic strain through heat treatment was representative of the shape 

memory effect. The high value of structural deformation at peak strength load capacity of the SMA test 

article further indicated an opportunity for high strain recovery (self-healing) upon thermal treatment. 

Using material parameters calibrated by ligament testing, the finite element modeling captured all of 

the main features of the lattice block deformation behavior, including deviations from non-linearity, strut 

buckling, lattice geometric effects, and even indications of strut fracture. The model can be used to design 

new lattice blocks that are optimized for weight and structural performance. 

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